Systems and methods for estimating heading and yaw rate for automated driving

ABSTRACT

Motion control systems and methods are provided in a vehicle. In one embodiment, a motion control system includes a controller. The controller is configured to: receive target trajectory data associated with an upcoming trajectory of the autonomous vehicle; determine a yaw rate reference and a relative heading reference associated with the upcoming target trajectory based on a numerical integration of the target trajectory data; and control a trajectory of the autonomous vehicle based on the yaw rate reference and the relative heading reference.

INTRODUCTION

The technical field generally relates to vehicle motion control systems,and more particularly relates to improving motion control systemperformance based on heading and yaw rate control references fortrajectory tracking.

Conventional heading and yaw rate references would be set equal to thetarget trajectory heading and the trajectory curvature. The headingreference is sometimes augmented by a steady-state sideslip angle tocompensate for the non-zero relative yaw angle during curve tracking.These approaches assume the references are quasi-steady and are validonly during highway driving. In low-speed maneuvering, the finite yawacceleration and rate of change of sideslip are significant.

Accordingly, it is desirable to provide improved heading and yaw ratereferences for trajectory tracking. It is further desirable to use thetrajectory tracking to improve motion control using the trajectorytracking. Furthermore, other desirable features and characteristics ofthe present disclosure will become apparent from the subsequent detaileddescription and the appended claims, taken in conjunction with theaccompanying drawings and the foregoing technical field and background.

SUMMARY

A motion control system is provided in a vehicle. In one embodiment, themotion control system including a controller. The controller isconfigured to: receive target trajectory data associated with anupcoming trajectory of the autonomous vehicle; determine a yaw ratereference and a relative heading reference associated with the upcomingtarget trajectory based on a numerical integration of the targettrajectory data; and control a trajectory of the autonomous vehiclebased on the yaw rate reference and the relative heading reference.

In various embodiments, the target trajectory data includes a desiredvehicle velocity.

In various embodiments, the target trajectory data includes a trajectorycurvature.

In various embodiments, the target trajectory data includes a roadbanking angle.

In various embodiments, the numerical integration is based on a bicyclemodel.

In various embodiments, the numerical integration of the yaw ratereference is based on:

${{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}\frac{C_{r}}{I_{zz}}}}},$where V_(x) represents a desired velocity, {dot over (κ)}_(d) representsa desired trajectory, ∅ represents a road banking angle, ψ representsthe yaw rate reference, m represents a mass of the autonomous vehicle, grepresents gravity, C_(r) represents a cornering stiffness on a reartire, L represents a vehicle wheel base, l_(r) represents a distancebetween a rear axle and a center of gravity, I_(zz) represents a vehiclemoment of inertia relative to a vertical axis, and l_(f) represents adistance between a front axes and the center of gravity.

In various embodiments, the numerical integration of the relativeheading reference is based on:

${\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - \frac{g\phi}{V_{x}}}},$where β represents relative heading, V_(x) represents a desiredvelocity, {dot over (κ)}_(d) represents a desired trajectory, ∅represents a road banking angle, ψ represents the yaw rate reference, mrepresents a mass of the autonomous vehicle, g represents gravity,C_(r)represents a cornering stiffness on a rear tire, L represents a vehiclewheel base, l_(r) represents a distance between a rear axle and a centerof gravity, I_(zz) represents a vehicle moment of inertia relative to avertical axis, and l_(f) represents a distance between a front axes andthe center of gravity.

In another embodiment a method includes: receiving, by a processor,target trajectory data associated with an upcoming trajectory of theautonomous vehicle; determining, by the processor, a yaw rate referenceand a relative heading reference associated with the upcoming targettrajectory based on a numerical integration of the target trajectorydata; and controlling, by the processor, a trajectory of the autonomousvehicle based on the yaw rate reference and the relative headingreference.

In various embodiments, the target trajectory data includes a desiredvehicle velocity.

In various embodiments, the target trajectory data includes a trajectorycurvature.

In various embodiments, the target trajectory data includes a roadbanking angle.

In various embodiments, the numerical integration is based on a bicyclemodel.

In various embodiments, the numerical integration of the yaw ratereference is based on:

${{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}\frac{C_{r}}{I_{zz}}}}},$where V_(x) represents a desired velocity, {dot over (κ)}_(d) representsa desired trajectory, ∅ represents a road banking angle, ψ representsthe yaw rate reference, m represents a mass of the autonomous vehicle, grepresents gravity, C_(r) represents a cornering stiffness on a reartire, L represents a vehicle wheel base, l_(r) represents a distancebetween a rear axle and a center of gravity, I_(zz) represents a vehiclemoment of inertia relative to a vertical axis, and l_(f) represents adistance between a front axes and the center of gravity.

In various embodiments, the numerical integration of the relativeheading reference is based on:

${\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - \frac{g\phi}{V_{x}}}},$where β represents relative heading, V_(x) represents a desiredvelocity, {dot over (κ)}_(d) represents a desired trajectory, ∅represents a road banking angle, ψ represents the yaw rate reference, mrepresents a mass of the autonomous vehicle, g represents gravity, C_(r)represents a cornering stiffness on a rear tire, L represents a vehiclewheel base, l_(r) represents a distance between a rear axle and a centerof gravity, I_(zz) represents a vehicle moment of inertia relative to avertical axis, and l_(f) represents a distance between a front axes andthe center of gravity.

In another embodiments, a non-transitory computer readable media encodedwith programming instructions configurable to cause a controller in avehicle to perform a method of motion control is provided. The methodincludes: receiving target trajectory data associated with an upcomingtrajectory of the autonomous vehicle; determining a yaw rate referenceand a relative heading reference associated with the upcoming targettrajectory based on a numerical integration of the target trajectorydata; and controlling a trajectory of the autonomous vehicle based onthe yaw rate reference and the relative heading reference.

In various embodiments, the target trajectory data includes a desiredvehicle velocity, a trajectory curvature, and a road banking angle.

In various embodiments, the numerical integration is based on a bicyclemodel.

In various embodiments, the numerical integration of the yaw ratereference is based on:

${{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}\frac{C_{r}}{I_{zz}}}}},$and wherein the numerical integration of the relative heading referenceis based on:

${\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - \frac{g\phi}{V_{x}}}},$where V_(x) represents a desired velocity, {dot over (κ)}_(d) representsa desired trajectory, ∅ represents a road banking angle, ψ representsthe yaw rate reference, m represents a mass of the autonomous vehicle, grepresents gravity, C_(r) represents a cornering stiffness on a reartire, L represents a vehicle wheel base, l_(r) represents a distancebetween a rear axle and a center of gravity, I_(zz) represents a vehiclemoment of inertia relative to a vertical axis, and l_(f) represents adistance between a front axes and the center of gravity.

In various embodiments, the numerical integrations are performed basedon a detected receding horizon, and initial conditions of the numericalintegrations are reinitialized at a start of the horizon and at everyloop time of the motion control.

In various embodiments, the numerical integrations are performed foreach point along a receding horizon independently of each other, andinitial conditions of the numerical integration are reinitialized at astart of the motion control.

BRIEF DESCRIPTION OF THE DRAWINGS

The exemplary embodiments will hereinafter be described in conjunctionwith the following drawing figures, wherein like numerals denote likeelements, and wherein:

FIG. 1 is a block diagram illustrating an autonomous vehicle having atrajectory tracking system in accordance with various embodiments;

FIG. 2 is a functional block diagram illustrating features of anautonomous driving system of the autonomous vehicle in accordance withvarious embodiments;

FIG. 3 is a dataflow diagram illustrating features of the trajectorytracking system of the autonomous driving system in accordance withvarious embodiments;

FIG. 4 is an illustration of a vehicle and vehicle dynamics inaccordance with various embodiments; and

FIGS. 5 and 6 are process flow charts depicting example processes fortrajectory tracking in accordance with various embodiments.

DETAILED DESCRIPTION

The following detailed description is merely exemplary in nature and isnot intended to limit the application and uses. Furthermore, there is nointention to be bound by any expressed or implied theory presented inthe preceding technical field, background, summary, or the followingdetailed description. As used herein, the term “module” refers to anyhardware, software, firmware, electronic control component, processinglogic, and/or processor device, individually or in any combination,including without limitation: application specific integrated circuit(ASIC), a field-programmable gate-array (FPGA), an electronic circuit, aprocessor (shared, dedicated, or group) and memory that executes one ormore software or firmware programs, a combinational logic circuit,and/or other suitable components that provide the describedfunctionality.

Embodiments of the present disclosure may be described herein in termsof functional and/or logical block components and various processingsteps. It should be appreciated that such block components may berealized by any number of hardware, software, and/or firmware componentsconfigured to perform the specified functions. For example, anembodiment of the present disclosure may employ various integratedcircuit components, e.g., memory elements, digital signal processingelements, logic elements, look-up tables, or the like, which may carryout a variety of functions under the control of one or moremicroprocessors or other control devices. In addition, those skilled inthe art will appreciate that embodiments of the present disclosure maybe practiced in conjunction with any number of systems, and that thesystems described herein is merely exemplary embodiments of the presentdisclosure.

For the sake of brevity, conventional techniques related to signalprocessing, data transmission, signaling, control, machine learningmodels, radar, lidar, image analysis, and other functional aspects ofthe systems (and the individual operating components of the systems) maynot be described in detail herein. Furthermore, the connecting linesshown in the various figures contained herein are intended to representexample functional relationships and/or physical couplings between thevarious elements. It should be noted that many alternative or additionalfunctional relationships or physical connections may be present in anembodiment of the present disclosure.

With reference to FIG. 1 , a trajectory tracking system shown generallyat 100 is associated with a vehicle 10 in accordance with variousembodiments. In general, the trajectory tracking system 100 receivesdata sensed from an environment of the vehicle 10, processes thereceived data to compute a reference heading and a reference yaw ratecoupled with host vehicle dynamics, which accounts for finite yawacceleration and varying sideslip angle during curve negotiation. Invarious embodiments, the tracking system 100 uses the references forsingle-point error-feedback of trajectory tracking, such as errorfeedback and feedforward, as well as receding horizon based optimalcontrol, such as model predictive control.

As depicted in FIG. 1 , the vehicle 10 generally includes a chassis 12,a body 14, front wheels 16, and rear wheels 18. The body 14 is arrangedon the chassis 12 and substantially encloses components of the vehicle10. The body 14 and the chassis 12 may jointly form a frame. The wheels16-18 are each rotationally coupled to the chassis 12 near a respectivecorner of the body 14.

In various embodiments, the vehicle 10 is an autonomous vehicle and thetrajectory tracking system 100 is incorporated into the autonomousvehicle 10 (hereinafter referred to as the autonomous vehicle 10). Theautonomous vehicle 10 is, for example, a vehicle that is automaticallycontrolled to carry passengers from one location to another. The vehicle10 is depicted in the illustrated embodiment as a passenger car, but itshould be appreciated that any other vehicle including motorcycles,trucks, sport utility vehicles (SUVs), recreational vehicles (RVs),marine vessels, aircraft, etc., can also be used. In an exemplaryembodiment, the autonomous vehicle 10 is a so-called Level Four or LevelFive automation system. A Level Four system indicates “high automation,”referring to the driving mode-specific performance by an automateddriving system of all aspects of the dynamic driving task, even if ahuman driver does not respond appropriately to a request to intervene. ALevel Five system indicates “full automation,” referring to thefull-time performance by an automated driving system of all aspects ofthe dynamic driving task under all roadway and environmental conditionsthat can be managed by a human driver.

As shown, the autonomous vehicle 10 generally includes a propulsionsystem 20, a transmission system 22, a steering system 24, a brakesystem 26, a sensor system 28, an actuator system 30, at least one datastorage device 32, at least one controller 34, and a communicationsystem 36. The propulsion system 20 may, in various embodiments, includean internal combustion engine, an electric machine such as a tractionmotor, and/or a fuel cell propulsion system. The transmission system 22is configured to transmit power from the propulsion system 20 to thevehicle wheels 16-18 according to selectable speed ratios. According tovarious embodiments, the transmission system 22 may include a step-ratioautomatic transmission, a continuously-variable transmission, or otherappropriate transmission. The brake system 26 is configured to providebraking torque to the vehicle wheels 16-18. The brake system 26 may, invarious embodiments, include friction brakes, brake by wire, aregenerative braking system such as an electric machine, and/or otherappropriate braking systems. The steering system 24 influences aposition of the of the vehicle wheels 16-18. While depicted as includinga steering wheel for illustrative purposes, in some embodimentscontemplated within the scope of the present disclosure, the steeringsystem 24 may not include a steering wheel.

The sensor system 28 includes one or more sensing devices 40 a-40 n thatsense observable conditions of the exterior environment and/or theinterior environment of the autonomous vehicle 10. The sensing devices40 a-40 n can include, but are not limited to, radars, lidars, globalpositioning systems, optical cameras, thermal cameras, ultrasonicsensors, and/or other sensors. The actuator system 30 includes one ormore actuator devices 42 a-42 n that control one or more vehiclefeatures such as, but not limited to, the propulsion system 20, thetransmission system 22, the steering system 24, and the brake system 26.In various embodiments, the vehicle features can further includeinterior and/or exterior vehicle features such as, but are not limitedto, doors, a trunk, and cabin features such as air, music, lighting,etc. (not numbered).

The communication system 36 is configured to wirelessly communicateinformation to and from other entities 48, such as but not limited to,other vehicles (“V2V” communication,) infrastructure (“V2I”communication), remote systems, and/or personal devices (described inmore detail with regard to FIG. 2 ). In an exemplary embodiment, thecommunication system 36 is a wireless communication system configured tocommunicate via a wireless local area network (WLAN) using IEEE 802.11standards or by using cellular data communication. However, additional,or alternate communication methods, such as a dedicated short-rangecommunications (DSRC) channel, are also considered within the scope ofthe present disclosure. DSRC channels refer to one-way or two-wayshort-range to medium-range wireless communication channels specificallydesigned for automotive use and a corresponding set of protocols andstandards.

The data storage device 32 stores data for use in automaticallycontrolling the autonomous vehicle 10. In various embodiments, the datastorage device 32 stores defined maps of the navigable environment. Invarious embodiments, the defined maps may be predefined by and obtainedfrom a remote system (described in further detail with regard to FIG. 2). For example, the defined maps may be assembled by the remote systemand communicated to the autonomous vehicle 10 (wirelessly and/or in awired manner) and stored in the data storage device 32. As can beappreciated, the data storage device 32 may be part of the controller34, separate from the controller 34, or part of the controller 34 andpart of a separate system.

The controller 34 includes at least one processor 44 and a computerreadable storage device or media 46. The processor 44 can be any custommade or commercially available processor, a central processing unit(CPU), a graphics processing unit (GPU), an auxiliary processor amongseveral processors associated with the controller 34, a semiconductorbased microprocessor (in the form of a microchip or chip set), amacroprocessor, any combination thereof, or generally any device forexecuting instructions. The computer readable storage device or media 46may include volatile and nonvolatile storage in read-only memory (ROM),random-access memory (RAM), and keep-alive memory (KAM), for example.KAM is a persistent or non-volatile memory that may be used to storevarious operating variables while the processor 44 is powered down. Thecomputer-readable storage device or media 46 may be implemented usingany of a number of known memory devices such as PROMs (programmableread-only memory), EPROMs (electrically PROM), EEPROMs (electricallyerasable PROM), flash memory, or any other electric, magnetic, optical,or combination memory devices capable of storing data, some of whichrepresent executable instructions, used by the controller 34 incontrolling the autonomous vehicle 10.

The instructions may include one or more separate programs, each ofwhich comprises an ordered listing of executable instructions forimplementing logical functions. The instructions, when executed by theprocessor 44, receive and process signals from the sensor system 28,perform logic, calculations, methods and/or algorithms for automaticallycontrolling the components of the autonomous vehicle 10, and generatecontrol signals to the actuator system 30 to automatically control thecomponents of the autonomous vehicle 10 based on the logic,calculations, methods, and/or algorithms. Although only one controller34 is shown in FIG. 1 , embodiments of the autonomous vehicle 10 caninclude any number of controllers 34 that communicate over any suitablecommunication medium or a combination of communication mediums and thatcooperate to process the sensor signals, perform logic, calculations,methods, and/or algorithms, and generate control signals toautomatically control features of the autonomous vehicle 10.

In various embodiments, as discussed in detail below, one or moreinstructions of the controller 34 are embodied in the trajectorytracking system 100 and, when executed by the processor 44, processsensor data with a bicycle model in order to determine a referencesvalues for heading and yaw rate, and use the reference values fortracking of the trajectory of the vehicle.

Referring now to FIG. 3 , and with continued reference to FIG. 1 , adataflow diagram illustrates various embodiments of an autonomousdriving system (ADS) 70 which may be embedded within the controller 34and which may include parts of the trajectory tracking system 100 inaccordance with various embodiments. That is, suitable software and/orhardware components of controller 34 (e.g., processor 44 andcomputer-readable storage device 46) are utilized to provide anautonomous driving system 70 that is used in conjunction with vehicle10.

Inputs to the autonomous driving system 70 may be received from thesensor system 28, received from other control modules (not shown)associated with the autonomous vehicle 10, received from thecommunication system 36, and/or determined/modeled by other sub-modules(not shown) within the controller 34. In various embodiments, theinstructions of the autonomous driving system 70 may be organized byfunction or system. For example, as shown in FIG. 3 , the autonomousdriving system 70 can include a computer vision system 74, a positioningsystem 76, a guidance system 78, and a vehicle control system 80. As canbe appreciated, in various embodiments, the instructions may beorganized into any number of systems (e.g., combined, furtherpartitioned, etc.) as the disclosure is not limited to the presentexamples.

In various embodiments, the computer vision system 74 synthesizes andprocesses sensor data and predicts the presence, location,classification, and/or path of objects and features of the environmentof the vehicle 10. In various embodiments, the computer vision system 74can incorporate information from multiple sensors, including but notlimited to, cameras, lidars, radars, and/or any number of other types ofsensors.

The positioning system 76 processes sensor data along with other data todetermine a position (e.g., a local position relative to a map, an exactposition relative to lane of a road, vehicle heading, velocity, etc.) ofthe vehicle 10 relative to the environment. The guidance system 78processes sensor data along with other data to determine a path for thevehicle 10 to follow. The vehicle control system 80 generates controlsignals for controlling the vehicle 10 according to the determined path.

In various embodiments, the controller 34 implements machine learningtechniques to assist the functionality of the controller 34, such asobstruction mitigation, route traversal, mapping, sensor integration,ground-truth determination, and feature detection, and objectclassification as discussed herein.

As mentioned briefly above, trajectory tracking system 100 of FIG. 1computes reference values for tracking the trajectory of the vehicle 10.All or parts of the trajectory tracking system 100 may be includedwithin, for example, the vehicle control system 80.

For example, as shown in more detail with regard to FIG. 3 and withcontinued reference to FIGS. 1 and 2 , the trajectory tracking system100 includes a model datastore 102, a yaw rate determination module 104,a relative heading determination module 106, and a trajectory controlmodule 108.

The model datastore 102 stores models for use in computing the referencevalues. In various embodiments, the models are based on a bicycle modeland the following relationships.

For example, as shown in FIG. 4 , an example bicycle model for thevehicle 10 includes:

${{\overset{˙}{V}}_{y} = {{{- V_{x}}\overset{˙}{\psi}} + {\frac{C_{f}}{m}( {\delta - \beta - \frac{l_{f}\overset{˙}{\psi}}{V_{x}}} )} + {\frac{C_{r}}{m}( {{- \beta} + \frac{l_{r}\overset{˙}{\psi}}{V_{x}}} )} - {g\phi}}},{and}$${\overset{¨}{\psi} = {{l_{f}\frac{C_{f}}{I_{zz}}( {\delta - \beta - \frac{l_{f}\overset{˙}{\psi}}{V_{x}}} )}{- {l_{r}\frac{c_{r}}{I_{zz}}( {{- \beta} + \frac{l_{r}\overset{˙}{\psi}}{V_{x}}} )}}}},$

where ∅ represents a road bank angle, δ represents the road wheel angle,V_(x) represents a desired velocity, {dot over (κ)}_(d) represents adesired trajectory, ψ represents the yaw rate reference, β represents asideslip angle β=V_(y)/V_(x), m represents a mass of the autonomousvehicle, g represents gravity, C_(r) represents corning stiffness of therear tires , L represents wheel base, l_(r) represents distance betweenvehicle rear axle and vehicle center of gravity (c.g.), I_(zz)represents moment of inertia around the vertical axis, and l_(f)represents distance between vehicle front axle and vehicle center ofgravity. Given the example bicycle model and the relation of thesideslip angle β to the kinematic course angle χ and the vehicle headingangle ψ, χ=β+ψ, and a kinematic constraint imposed such that the changein vehicle course aligns with a target curvature κ_(d) as {dot over(χ)}=κ_(d)V_(x), a resulting yaw rate model is:

$\begin{matrix}{{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}{\frac{C_{r}}{I_{zz}}.}}}} & (1)\end{matrix}$

With the appropriate initial conditions, the yaw rate model is astandalone differential equation with a solution, {dot over (ψ)}(t) thatprovides the yaw rate reference along the target trajectory. Thus, theyaw rate reference can be obtained through numerical integration of theyaw rate model of equation (1).

Provided the above yaw rate model, a relative heading model can bederived from the relation: {dot over (β)}={dot over (χ)}−{dot over (ψ)},as:

$\begin{matrix}{\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - {\frac{g\phi}{V_{x}}.}}} & (2)\end{matrix}$

Likewise, the relative heading reference can be obtained throughnumerical integration of the relative heading model of equation (2). Invarious embodiments, the instructions for carrying out the models (1)and (2) are stored in the model datastore 102 as yaw rate model data 110and relative heading model data 112.

In various embodiments, the yaw rate determination module 104 receivesas input desired velocity data 114, trajectory curvature data 116, androad banking data 118. The yaw rate determination module 104 computesthe yaw rate reference and yaw acceleration based on the received data114-118 and numerical integration of the yaw rate model data 110 fromthe model datastore 102. The yaw rate determination module 104 providesyaw reference data 120 based on the computed values.

For example, the yaw rate references can be computed along a recedinghorizon by solving the yaw rate model (1) numerically for each pointalong the receding horizon. In such example, the yaw rate references arere-initialized and re-computed for every instance of the controlroutine.

In another example, the yaw rate references can be computed along areceding horizon by solving the yaw rate model (1) for each predictionpoint independently by integrating the point data in real time. As canbe appreciated, other methods of numerically integrating the yaw ratereference model can be implemented in accordance with the variousembodiments as the disclosure is not limited to the present examples.

In various embodiments, the relative heading determination module 106receives as input the desired velocity data 114, the yaw rate referencedata 120, and the road banking data 118. The relative headingdetermination module 106 computes a relative heading reference based onthe received data 114, 120, 118 and numerical integration of therelative heading model data 112 from the model datastore 102. Therelative heading determination module 106 provides relative headingreference data 122 based on the computed values.

For example, the relative heading references can be computed along areceding horizon by solving the relative heading model (2) numericallyfor each point along the receding horizon. In such example, the relativeheading references are re-initialized and re-computed for every instanceof the control routine.

In another example, the relative heading references can be computedalong a receding horizon by solving the relative heading model (2) foreach point independently by integrating the point data in real time. Ascan be appreciated, other methods of numerically integrating the yawrate reference model can be implemented in accordance with the variousembodiments as the disclosure is not limited to the present examples.

In various embodiments, the trajectory control module 108 receives asinput the yaw reference data 120 and the relative heading reference data122. The trajectory control module 108 tracks the trajectory of thevehicle 10 along the desired curve based on the received input 120, 122.For example, when the yaw rate reference and the relative headingreference are solved according to the first method, the trajectorycontrol module 108 uses model predictive control and the yaw ratereference, and the relative heading reference to generate controlsignals 124 control the trajectory. In another example, when the yawrate reference and the relative heading reference are solved accordingto the second method, the trajectory control module 108 uses errorfeedback or feed forward control and the yaw rate reference, and therelative heading reference to generate control signals 124 control thetrajectory. As can be appreciated, other control methods can beimplemented in accordance with the various embodiments as the disclosureis not limited to the present examples.

Referring now to FIGS. 5 and 6 , and with continued reference to FIGS.1-4 , flowcharts illustrate a process 400 and a process 500 that can beperformed by the trajectory tracking system 100 of FIG. 1 in accordancewith the present disclosure. As can be appreciated in light of thedisclosure, the order of operation within the processes 400, 500 is notlimited to the sequential execution as illustrated in FIGS. 5 and 6 ,but may be performed in one or more varying orders as applicable and inaccordance with the present disclosure. In various embodiments, theprocesses 500, 600 can be scheduled to run based on one or morepredetermined events, and/or can run continuously during operation ofthe autonomous vehicle 10.

In one embodiment, the process 400 may begin at 405. The input dataincluding the desired velocity data, the trajectory curvature data, andthe road banking data is received at 410. For each point along thetrajectory curvature (k0, k1, k2, . . . kn) at 420, the yaw ratereference is computed through numerical integration of the yaw ratemodel at 430, and the relative heading reference is computed throughnumerical integration of the relative heading model at 440. Once thereference values are computed for each point at 420, the referencevalues are used to track the vehicle's trajectory using, for example,model predictive control at 450. Thereafter, the process 400 may end at460.

In another embodiment, the process 500 may begin at 505. The input dataincluding the desired velocity data, the trajectory curvature data, andthe road banking data is received at 510. A next point along thetrajectory curvature is selected and the yaw rate reference is computedfor the point in real time through numerical integration at 520. Therelative heading reference is computed for the point in real timethrough numerical integration at 530. The reference values are used totrack the vehicle's trajectory using, for example, error feedbackcontrol and/or feedforward control at 540. Thereafter, the process 500may end at 550.

While at least one exemplary embodiment has been presented in theforegoing detailed description, it should be appreciated that a vastnumber of variations exist. It should also be appreciated that theexemplary embodiment or exemplary embodiments are only examples, and arenot intended to limit the scope, applicability, or configuration of thedisclosure in any way. Rather, the foregoing detailed description willprovide those skilled in the art with a convenient road map forimplementing the exemplary embodiment or exemplary embodiments. Itshould be understood that various changes can be made in the functionand arrangement of elements without departing from the scope of thedisclosure as set forth in the appended claims and the legal equivalentsthereof.

What is claimed is:
 1. A motion control system of an autonomous vehicle,the motion control system comprising a controller, the controllerconfigured to: receive target trajectory data associated with anupcoming trajectory of the autonomous vehicle; determine a yaw ratereference and a relative heading reference associated with the upcomingtarget trajectory based on a numerical integration of the targettrajectory data; and control a trajectory of the autonomous vehiclebased on the yaw rate reference and the relative heading reference. 2.The motion control system of claim 1, wherein the target trajectory dataincludes a desired vehicle velocity.
 3. The motion control system ofclaim 1, wherein the target trajectory data includes a trajectorycurvature.
 4. The motion control system of claim 1, wherein the targettrajectory data includes a road banking angle.
 5. The motion controlsystem of claim 1, wherein the numerical integration is based on abicycle model.
 6. The motion control system of claim 5, wherein thenumerical integration of the yaw rate reference is based on:${{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}\frac{C_{r}}{I_{zz}}}}},$where V_(x) represents a desired velocity, {dot over (κ)}_(d) representsa desired trajectory, ∅ represents a road banking angle, ψ representsthe yaw rate reference, m represents a mass of the autonomous vehicle, grepresents gravity, C_(r) represents a cornering stiffness on a reartire, L represents a vehicle wheel base, l_(r) represents a distancebetween a rear axle and a center of gravity, I_(zz) represents a vehiclemoment of inertia relative to a vertical axis, and l_(f) represents adistance between a front axes and the center of gravity.
 7. The motioncontrol system of claim 5, wherein the numerical integration of therelative heading reference is based on:${\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - \frac{g\phi}{V_{x}}}},$where β represents relative heading, V_(x) represents a desiredvelocity, {dot over (κ)}_(d) represents a desired trajectory, ∅represents a road banking angle, ψ represents the yaw rate reference, mrepresents a mass of the autonomous vehicle, g represents gravity,C_(r)represents a cornering stiffness on a rear tire, L represents a vehiclewheel base, l_(r) represents a distance between a rear axle and a centerof gravity, I_(zz) represents a vehicle moment of inertia relative to avertical axis, and l_(f) represents a distance between a front axes andthe center of gravity.
 8. A method in a vehicle for exercising motioncontrol, the method comprising: receiving, by a processor, targettrajectory data associated with an upcoming trajectory of the autonomousvehicle; determining, by the processor, a yaw rate reference and arelative heading reference associated with the upcoming targettrajectory based on a numerical integration of the target trajectorydata; and controlling, by the processor, a trajectory of the autonomousvehicle based on the yaw rate reference and the relative headingreference.
 9. The method of claim 8, wherein the target trajectory dataincludes a desired vehicle velocity.
 10. The method of claim 8, whereinthe target trajectory data includes a trajectory curvature.
 11. Themethod of claim 8, wherein the target trajectory data includes a roadbanking angle.
 12. The method of claim 8, wherein the numericalintegration is based on a bicycle model.
 13. The method of claim 12,wherein the numerical integration of the yaw rate reference is based on:${{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}\frac{C_{r}}{I_{zz}}}}},$where V_(x) represents a desired velocity, {dot over (κ)}_(d) representsa desired trajectory, ∅ represents a road banking angle, ψ representsthe yaw rate reference, m represents a mass of the autonomous vehicle, grepresents gravity, C_(r) represents a cornering stiffness on a reartire, L represents a vehicle wheel base, l_(r) represents a distancebetween a rear axle and a center of gravity, I_(zz) represents a vehiclemoment of inertia relative to a vertical axis, and l_(f) represents adistance between a front axes and the center of gravity.
 14. The methodof claim 12, wherein the numerical integration of the relative headingreference is based on:${\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - \frac{g\phi}{V_{x}}}},$where β represents relative heading, V_(x) represents a desiredvelocity, {dot over (κ)}_(d) represents a desired trajectory, ∅represents a road banking angle, ψ represents the yaw rate reference, mrepresents a mass of the autonomous vehicle, g represents gravity, C_(r)represents a cornering stiffness on a rear tire, L represents a vehiclewheel base, l_(r) represents a distance between a rear axle and a centerof gravity, I_(zz) represents a vehicle moment of inertia relative to avertical axis, and l_(f) represents a distance between a front axes andthe center of gravity.
 15. A non-transitory computer readable mediaencoded with programming instructions configurable to cause a controllerin a vehicle to perform a method for motion control, the methodcomprising: receiving target trajectory data associated with an upcomingtrajectory of the autonomous vehicle; determining a yaw rate referenceand a relative heading reference associated with the upcoming targettrajectory based on a numerical integration of the target trajectorydata; and controlling a trajectory of the autonomous vehicle based onthe yaw rate reference and the relative heading reference.
 16. Thenon-transitory computer readable media of claim 15, wherein the targettrajectory data includes a road banking angle, a desired vehiclevelocity, and a trajectory curvature.
 17. The non-transitory computerreadable media of claim 15, wherein the numerical integration is basedon a bicycle model.
 18. The non-transitory computer readable media ofclaim 15, wherein the numerical integration of the yaw rate reference isbased on:${{\overset{˙}{\psi}( {s^{2} + {l_{r}\frac{LC_{r}}{I_{zz}V_{x}}s} + {L\frac{C_{r}}{I_{zz}}}} )} = {{l_{f}\frac{m}{I_{zz}}( {{{\overset{˙}{\kappa}}_{d}V_{x}^{2}} + {g\overset{˙}{\phi}}} )} + {LV_{x}\kappa_{d}\frac{C_{r}}{I_{zz}}}}},$and wherein the numerical integration of the relative heading referenceis based on:${\overset{˙}{\beta} = {{{- \frac{LC_{r}}{l_{f}mV_{x}}}\beta} + {\overset{¨}{\psi}\frac{I_{zz}}{l_{f}mV_{x}}} + {\overset{˙}{\psi}( {{l_{r}\frac{LC_{r}}{I_{zz}V_{x}^{2}}} - 1} )} - \frac{g\phi}{V_{x}}}},$where V_(x) represents a desired velocity, {dot over (κ)}_(d) representsa desired trajectory, ∅ represents a road banking angle, ψ representsthe yaw rate reference, m represents a mass of the autonomous vehicle, grepresents gravity, C_(r) represents a cornering stiffness on a reartire, L represents a vehicle wheel base, l_(r) represents a distancebetween a rear axle and a center of gravity, I_(zz) represents a vehiclemoment of inertia relative to a vertical axis, and l_(f) represents adistance between a front axes and the center of gravity.
 19. Thenon-transitory computer readable media of claim 18, wherein thenumerical integrations are performed based on a detected recedinghorizon, and wherein initial conditions of the numerical integrationsare reinitialized at a start of the horizon and at every loop time ofthe motion control.
 20. The non-transitory computer readable media ofclaim 18, wherein the numerical integrations are performed for eachpoint along a receding horizon independently of each other, and whereininitial conditions of the numerical integration are reinitialized at astart of the motion control.